The homotopy perturbation method for fractional differential equations: part 2, two-scale transform

Purpose - The purpose of this paper is to find an approximate solution of a fractional differential equation. The fractional Newell-Whitehead-Segel equation (FNWSE) is used to elucidate the solution process, which is one of the nonlinear amplitude equation, and it enhances a significant role in the modeling of various physical phenomena arising in fluid mechanics, solid-state physics, optics, plasma physics, dispersion and convection systems. Design/methodology/approach - In Part I. the authors adopted Mohand transform to find the analytical solution of FNWSE. In this part, the authors apply the fractional complex transform (the two-scale transform) to convert the problem into its differential partner, and then they introduce the homotopy perturbation method (HPM) to bring down the nonlinear terms for the approximate solution. Findings - The HPM makes numerical simulation for the fractional differential equations easy, and the two-scale transform is a strong tool for fractal models. Originality/value - The HPM with the two-scale transform sheds a bright light on numerical approach to fractional calculus.